E

F

I

H

G

J

M

L

K

a

b

Formule : (a+b)²=...

a²

ab

ab

b²

En\ exprimant\ de\ deux\ façons\ différentes\ 
l'aire\ du\ grand\ carré\ EIKM,\
trouver\ la\ formule\ donnant\ la\ forme\
développée\ de\ (a+b)².\

(a+b)²=a²+2ab+b²

Afficher la réponse

MathsEnClair.com

G

a = 2.3 (slider from 0 to 5, step 0.1)
b = 3.2 (slider from 0 to 5, step 0.1)
E = (-3.62, 5.06)
c_1: abs(a)
F = Point(Circle[E, abs(a)])
c = Segment(E, F)
d = Ray(E, F)
e = Circle(F, b)
I = Intersect(e, d, 2)
f = OrthogonalLine(E, c)
g = Circle(E, a)
H = Intersect(g, f, 1)
h = OrthogonalLine(H, f)
i = OrthogonalLine(F, d)
k = Circle(H, b)
M = Intersect(k, f, 1)
j = OrthogonalLine(M, f)
l = OrthogonalLine(I, d)
G = Intersect(h, i)
J = Intersect(h, l)
L = Intersect(i, j)
poly1, a_1, d_1, f_1, b_1 = Polygon(E, H, G, F)
poly2, b_2, f_2, g_1, c_2 = Polygon(F, G, J, I)
poly3, d_2, e_1, h_1, f_3 = Polygon(H, M, L, G)
K = Intersect(j, l)
poly4, h_2, i_1, g_2, f_4 = Polygon(L, K, J, G)
α = Angle(H, E, F)
β = Angle(F, I, J)
γ = Angle(J, K, L)
δ = Angle(L, M, H)
A = Midpoint(c)
B = Midpoint(c_2)
C = Midpoint(E, G)
D = Midpoint(F, J)
N = Midpoint(H, L)
O = Midpoint(G, K)
m = false